Would you post the model number. Your task is to determine exactly where the water is coming from. It could be at the hose to black plastic connection or the connection of the black plastic to the metal frame. Not seeing your picture, I am flying on instruments in this reply. If possible, get a rag ...

With the house up to the set temperature and the furnace off, at the thermostat set the FAN from AUTO to ON. As the fan runs do you hear the noises? If so, they could be the duct work flexing, usually the plenum chamber. Google the term "oil canning".

The original installers did a poor job and possibly one not up to the current building code standards. I have a feeling the installers were lazy and didn't expect the type of cold weather you're having now. Any and all lines that drain water should be pitched properly to their terminus.

You wrote,"So the burners are lighting up. They stay lit for approx 3 mins then goes out and the fan keeps running blowing warm air for approx 7 mins after the burners go out." That is a symptom of either a heat exchanger overheating (not enough air flow due to dirty filters, collapsed ducting or ot...

I find it hard to believe your furnace "blows heat" with only a pilot light as the heat source. What is the make and model of the furnace? What are the outdoor temperatures today, Jan. 1? Does the furnace keep your house warm? What temperature is your thermostat set at?

You really need to refer to the installation manual. However you can get an idea by looking at the diameter of the diameter of the vent at the furnace where you'd connect continuing vent pipe. If at the furnace it's 4" take-off then I would THINK a 4" vent world be okay. You can try it and CAREFULLY...

Not knowing your roof design or prevailing winds that's not an easy question. The manufacturer of the new furnace should have guidelines for the venting of the furnace. Absent those you can try shortening the vent and see how it all works. Just don't use PVC cement until you know all is working. Tha...